code: def _nls_jacobian_func(
      tensor_elements,
      design_matrix,
      data,
      Diso=3e-3,
      weighting=None,
      sigma=None,
      cholesky=False,
      f_transform=False,
  ):
      """The Jacobian is the first derivative of the least squares error
      function.
  
      Parameters
      ----------
      tensor_elements : array (8, )
          The six independent elements of the diffusion tensor followed by
          -log(S0) and the volume fraction f of the water elimination
          compartment. Note that if f_transform is true, volume fraction f is
          converted to ft = arcsin(2*f - 1) + pi/2
      design_matrix : array
          The design matrix
      Diso : float, optional
          Value of the free water isotropic diffusion. Default is set to 3e-3
          $mm^{2}.s^{-1}$. Please adjust this value if you are assuming different
          units of diffusion.
      f_transform : bool, optional
          If true, the water volume fraction was converted to
          ft = arcsin(2*f - 1) + pi/2, insuring f estimates between 0 and 1.
          See fwdti.nls_fit_tensor
          Default: True
      """
      tensor = np.copy(tensor_elements)
      if f_transform:
          f = 0.5 * (1 + np.sin(tensor[7] - np.pi / 2))
      else:
          f = tensor[7]
  
      t = np.exp(np.dot(design_matrix, tensor[:7]))
      s = np.exp(
          np.dot(
              design_matrix,
              np.array([Diso, 0, Diso, 0, 0, Diso, tensor[6]]),
          )
      )
      T = (f - 1.0) * t[:, None] * design_matrix
      S = np.zeros(design_matrix.shape)
      S[:, 6] = f * s
  
      if f_transform:
          df = (t - s) * (0.5 * np.cos(tensor[7] - np.pi / 2))
      else:
          df = t - s
      return np.concatenate((T - S, df[:, None]), axis=1)
  
imports: import warnings
  import numpy
  import scipy.optimize
  from dipy.reconst.base import ReconstModel
  from dipy.reconst.dti import TensorFit, design_matrix, decompose_tensor, _decompose_tensor_nan, from_lower_triangular, lower_triangular
  from dipy.reconst.dki import _positive_evals
  from dipy.reconst.vec_val_sum import vec_val_vect
  from dipy.core.ndindex import ndindex
  from dipy.core.gradients import check_multi_b
  from dipy.reconst.multi_voxel import multi_voxel_fit
label_desc: Use image node_id 5 for calling a global function with example usage: _nls_jacobian_func(tensor_elements, design_matrix, data, Diso, weighting, sigma, cholesky, f_transform) and returns: np